RATIOS AND SQUARES

Pi is a constant, in a circle. But why is the ratio of area of a square to diagonal length not a constant? But ratio of diagonal length to side is?

MATH AND GAMBLING 21 the movie

21 the movie came out and I recommend it as a go-see. Might have been a better plot without the bit of violence.

But you will find some convincing links between the math and the gambling.

A math professor and a group of his students create an informal club. Complete with weekend outings to Las Vegas.

As you work through a 21 deck, the remaining cards can become skewed. Depending on face cards already played. Thus a table becomes "hot" and more likely to 21.

TILING PROBLEM IN CONSTRUCTION OF WALL

Notice the many different size bricks in the wall and the tiling problem it represents. This is an old building, couple stories tall.

THE ETERNITY II PUZZLE

The puzzle is composed of 256 square pieces, edges have to match. My approach?
Find the correct orientation for each piece. So that all pieces are balanced. I use a
two part approach, one that looks very carefully at how the pieces match up. It
then repeats that in the algorithm. The second part asks: If I have a square made
up of four squares, which square is filled by the puzzle piece. This second part does a Parity
Balance.

In Summary: Which Quadrant does the piece occupy, and which orientation in the Quadrant does it occupy?